- may misc reserves quite small and tedious/difficult to calculate exactly
- in practice - less precise techniques used, such as
- single average age
- single set of factors for range of policy forms

- in practice - less precise techniques used, such as
- Valn Actuary must be prepared to show that these approximations do not significantly overstate reserve liabs

- reserves in attidion to basic reserves w/ gross premiums < certain level
- US
- prior to 1976 - SVL stated V_def(x) req'd if gross prem < valn net prem (if valn net prem used)
- criticisms
- reserve strengthening could cause basic policy reserve to increase. GP could be sufficient at old rate and not under lowered rate
- having conservative reserve basis sometimes caused def reserves and wouldn't be req'd w/ more agressive reserves
- V_def(x) not allowed as a tax reserve

- 76 amendments removed specific references to V_def(x), but basic reserves req'd to be increased in certain instances
- reserve is max(a,b)
- a - Vx calculated according to method, mort table and int rate actually used for policy
- b - Vx calculated by policy method, using min valn standards for mort, int and max(valn net prem, gross prem) each year
- excess of b over a is referred to as V_def(x) everywhere except SVL
- since part of Vx definition, gets tax credit

- Def Reserves don't follow usual pattern of prem paying life reerves
- generally have max value at issue and decrease w/ time

- because of resulting surplus strain - try to design product w/o (or minimal) def Vx

- Practical Considerations of Def Reserves
- GP is total annualized GP for policy, including modal loading and policy fee
- premiums for benefit/riders not included, but deficiencies in base can be offset by sufficiencies in riders
- because of these complications, usually calc these reserves via seriatim method
- many co's continue to calc using the old method. Produces teh exact same reserve in typical case

- Def Reserves for Renewable Term Policies
- old school - series of sep policies for reserve purposes - never V_def(x) for ART until mid-70s
- late 70s - early 80s - lower ART rates, regulators concerned, state regs said to consider it an ongoing policy
- 2 methods for looking at valn prems for ART
- Unitary Method - considers entire stream of future gross prems & develops proportional set of valn net prems
- Term Method - looks at each renewal period separately

- Unitary Method fell into disfavor w/ regulators since ultra high prem @ old ages offset deficiencies at early ages
- AG4 (1984) - term policies w/o CV - req'd add'l reserve if future guar prems < valn net prems as calced using a special basis in AG4
- Valn Model Reg (1995) - Contract Segmentation Method
- G(t) = GP(x+k+t) / GP(x+k+t-1)
- R(t) = q(x+k+t) / q(x+k+t-1)
- GP is guar gross prem w/o policy fee (if pol fee is level) - NY says uses current prem
- q(x+t) = valn mort rate for def reserves
- each time G(t) > R(t) a new segement is created +/-1% on R(t) to avoid new segments b/c of rounding
- basic reserves calced for each segment, EA_CRVM only for first segment
- Valn net prems a constant % of gross
- ex. 10 yr renewable term - CRVM first seg, NL thereafter

- Valn Model Reg - Vx = max(unitary, segmented) for each dur
- n-year renewable term w/ non-deficient guar prems exempt & some AA YRT

- Def reserves calculated as per 76 amendments using gross instead of net
- 5 year safe harbor if 1st segment < 5 years, don't have to use gross, even if deficient
- actuary must opine that reserves are sufficient

- Valn Model Reg allows updated selection factors in calc of basic reserves
- even lower selection factors OK for def reserves

- 5 year safe harbor if 1st segment < 5 years, don't have to use gross, even if deficient

- Canadian Practice for Renewable Term Policies
- Valn Tech Paper #2
- valued to end of benefit period, not renewal
- excess of heaped @ renewal over normal renew comm may be treated as issue expense
- how-to calc valn net prem if gross not level is described
- lapse rates can spike @ renewals if prem increases
- re-entry proportion (% of PO who will requalify for select @ rentry)

- Valn Tech Paper #2
- Alternative Min Reserves for UL (AMR)
- these are UL equiv to def reserves and covered in Chapter 4

- Usually calced using 1959 ADB tables
- calced using same methodology
- [t]V_ADB(x) = [1000*(M_ADB(x+t)-M_ADB(x+n)) - P_ADB(x)(N(x) - N(x+m)]/D(x+t)
- P_ADB(x) = [1000(M_ADB(x)-M_ADB(x+n)]/(N(x) - N(x+m))
- M_ADB(x) = sum(v*q_adb(x)*D(x))
- many approximations used, often w/ age and plan groupings

- SVL - reserve using Period 2 disablement rates of SOA 1952 disability study
- Active Life Reserves
- what prem to waive - gross or net w/ or w/o wvr prem w/ or w/o other (ADB etc) prems
- usually gross since commissions and what not still paid & ususally other benefits as well
- many approximations used
- reserves shoudl reflect prems (ex increasing if ART)
- UL policies - two types
- waiver of COI
- waiver of planned premium

- Disabled Life Reserves
- consists of 4 types of claims
- approved, in course of settlement (ICOS), resisted, incurred but not reported (IBNR)
- ICOS, resisted, IBNR considered policy claim liabilities
- valuation of approved claims
- disabled life annuities using tables mentioned in SVL and appropriate valn int rate
- these factors applied to amount being waived
- adue([x+0.5]+n-.5:t-.5|) where
- x - insurance anniv prior to dis
- n - policy year of dis
- t - # years benefits run, from pol anniv in year of valn

- normally use a seriatim valuation

- consists of 4 types of claims
- Disability and Death of Payor Benefits
- typically waives prem to child's age 21 or 25
- theoretical reserve complicated since 2 lives involved
- if dis payor, both death and dis must be considered
- essentially decreasing term so small or negative reserves expected
- approximations normally used
- usually ignore child's mortality
- often hold 1/2 gross prem of payor benefit as reserve
- reserve after death of payor is an annuity for remaining premiums
- often mortality is ignored and annuity certain used

- term reserve for amt of ins = (m-1)/2m * P_modal <- net prem
- once common approximation
- for each reserve basis, select a few major plans or key ages
- calc S_tot (amt of ins) G_tot (gross AP) P_tot (net AP) and V_tot (base reserve)
- Gbar = G_tot / S_tot Pbar = P_tot / S_tot (avg gross and net prem per $1m)
- pick xbar where Pbar and Gbar are approx the same (find age that has these prems)

- Vbar = V_tot / S_tot using xbar and Vbar, find approx tbar (dur)
- using xbar, tbar calc [tbar]V'(xbar:n|) where n is orig prem pay period of paln (term reserve factor)
- multiply term reserve factor by P_tot

- after doing for each grouping
- avg non-ded reserve factor is b/a
- a = sum(P_tot) and b = sum(P_tot*[tbar]V'(xbar:n|)) across all plans
- this factor applied to total net def prems for all plans w/in reserve basis

- for each reserve basis, select a few major plans or key ages
- Surrender Values in Excess of Reserves
- excess of SV over Vx needs to be carried in 8G
- based on seriatim, no offsetting overage w/ underages

- Valn Technique Paper #1 - Valn of Lapse-Supported Products
- established b/c Canadian Actuaries can recognize lapses in valn
- <maybe revisit this if applicable to 8I-U>

- Traditional
- pays small db or becomes paid up @ first death
- valued as single life after first death

- Frasier-Type
- no change of status @ first death
- valued independently of wheter a death death has occurred

- Reserves for Traditional Policies
- if paid up @ first death A(x+t:y+t)bar - P*adue(x+t:y+t)
- if pays x% @ first death and 100% at second death A(x+t:y+t)bar + xA(x+t:y+t) - P*adue(x+t:y+t)bar
- after first death A(y_t) if paid up, A(y+t) - P*adue(y+t) otherwise

- Reserves for Frasier-Type Policies
- l([x]+t:[y]+t)bar = l(xy)bar*([t]p(x) + [t]p(y) - [t]p(xy)
- A([x]+t:[y]+t)bar - P*adue([x]+t:[y]+t)bar
- joint equal age (JEA) often used to simplify calculation
- AG20 - acceptable rules for JEA 80CSO for First-to-Die
- many cos use these same rules for Last-to-Die

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